Luckily for us our old 169 model Panda (2010) doesn't have stop start!
but my boy's 2012 Punto does. the car was bought used and the stop star never worked. About 2 years later the car started failing to start when left for a couple of days or when the weather was very cold. Bought a new battery and the stop start has worked ever since - until a few months ago when the Blue and Me failed and is now putting a parasitic overnight drain on the battery.
I really dislike stop start for a number of reasons. Of course, as you mention, it can be caught out but I also feel for the flywheel ring gear and starter pinion. I also wonder about the advisability of it's use on turboed engines where any reduction in oilflow to the turbo must be detrimental. So I always disabled it on the Ibiza and now I'm doing the same with my new Scala. The Scala has given me another one to disable on start up - Lane Assist!